75.1.6 problem 7

Internal problem ID [16669]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 09:16:52 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 8

dsolve(diff(y(x),x)=sqrt(1-y(x)^2),y(x), singsol=all)
 

\[ y = \sin \left (x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.157 (sec). Leaf size: 28

DSolve[D[y[x],x]==Sqrt[1-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sin (x+c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}